Þorleikr’s background is unknown. In 1051 he travelled from Iceland via Norway to Denmark to present a poem to Sveinn Úlfsson (ÍF 28, 113; ÍF 29, 253; Mork 1928-32, 161; Flat 1860-8, III, 338; Fms6, 256). Both his name and his nickname fagri ‘the Fair’ indicate that he may have come from the family of the Laxdœlir (see Genealogy IIIa in ÍF 5; SnE 1848-87, III, 737-9; LH 1894-1901, I, 641-2). Þorleikr was a rather common name among the Laxdœlir (e.g. Þorleikr Hǫskuldsson and Þorleikr Bollason), and members of that family, such as Hǫskuldr Dala-Kollsson, Óláfr pá ‘Peacock’ Hǫskuldsson and Hallgerðr Hǫskuldsdóttir, were admired for their beauty (see ÍF 5, 14, 27; ÍF 12, 6-7). Þorleikr is listed in Skáldatal as one of the poets who eulogised Sveinn Úlfsson, and it is not said that he composed about any other dignitary or ruler (see SnE 1848-87, III, 258, 267, 283).